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Mathematical Tools for Computer Vision

University of Science and Technology
Electronics and Telecommunications Research Institute (ETRI)
Vision System Research Team, Jae-Young LEE
March 1, 2016 ~ June 24, 2016
https://sites.google.com/site/roricljy/


1. Geometry: Vectors
   - Vector & Scalar & Vector Equality, Addition, and Subtraction
   - Euclidean Vector
   - Trigonometry Review
   - Polar Representation
   - Dot product & Cross product
   - Homework #1
   - Homework #2



2. Geometry: 공간 도형
   - 도형
   - 직선의 방정식
   - 평면의 방정식
   - 부등식의 영역
   - 도형의 방정식과 함수
   - Homework #3



3. 행렬 연산
   - Introduction
   - Matrices and matrix algebra
   - Matrices and systems of linear equations



4. 벡터공간, 선형시스템
   - Vector Spaces
   - Basis and Dimension
   - Rank of a Matrix and Systems of Linear Equations
   - 기타 선형대수학에서 알아두어야 할 것들
   - Homework #4
   - Homework #5



5. 고유값분해, 주성분분석, 특이값분해
   - Eigenvalue and Eigenvector
   - Eigendecomposition
   - PCA (Principal Component Analysis)
   - SVD (Singular Value Decomposition)
   - Homework #7 (SVD를 이용한 직선, 원, 타원 근사)



6. 파라미터 추정과 최소 자승법
   - 파라미터 추정 기초
   - 최소 자승법 기초
   - Homework #8 (최소자승법을 이용한 영상 이진화)



7. Robust 파라미터 추정 기법
   - M-estimator (Weighted LS)
   - RANSAC
   - Homework #9 (LS, M-estimtor, RANSAC을 이용한 불균일 영역 검출)



8. 최적화 기법
   - 일차미분(Gradient descent)을 이용한 최적화
   - 이차미분(Newton)을 이용한 최적화 (2차 Taylor 근사)
   - 최적화 보완 기법 (Trust Region, Line Search, Saddle-free Newton)
   - 다변수함수에서의 최적화
   - LS 문제에 특화된 기법 (Gauss-Newton, Levenberg-Marquardt)
   - Homework #10 (원 근사 or 최적화, Gradient descent와 Gauss-newton 방법 사용)



9. 기계 학습 기법
   - 기계학습 기초
   - Gaussian Mixture Model 등 여러가지 알고리즘





Review
After taking this course, I can get knowledge of linear algebra such as vectors, matrices, eigen-decomposition, parameter estimation, Principal Component Analysis, Singular Value Decomposition, optimization techniques and so on and the computer vision. Actually, every class, we learn some linear algebra and we apply it to computer vision domain in order to solve the problem. It's very interesting because it is not only mathematics, but it's real world techniques of computer vision problems by using OpenCV or MATLAB. In this process, I could easily understand the concepts and have even intuition for difficult concepts.

One of the important knowledge is a way of solving linear or non-linear algebra system. Since in the real world, there are many problems of linear algebra system. So, given the knowledge, I could represent the problem to matrices (linear algebra representation) and know how to solve it even the non-linear case.

Taking this opportunity, the interest of linear algebra is increased more and more. I want to deep understand of the concepts. Linear algebra field is very interesting.  


Reference
[1] 다크프로그래머, http://darkpgmr.tistory.com/





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